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%I #38 Mar 17 2021 03:25:03
%S 6,9,5,7,4,3,5,8,9,3,9,2,5,2,1,7,4,6,2,4,6,6,0,9,0,0,6,7,8,2,9,1,8,5,
%T 3,0,4,1,3,0,6,6,5,9,2,7,6,6,6,0,1,3,3,3,6,3,1,4,6,0,8,0,9,5,7,3,9,3,
%U 0,1,7,5,2,9,4,5,0,8,4,1,4,1,7,3,5,9,2,0,4,7,8,5,2,5,3,0,6,0,7,4,3,2,9,1,6
%N Decimal expansion of Product_{p = prime} (1 + 6/p^2).
%H Pieter Moree, <a href="https://doi.org/10.1007/s002290050222">Approximation of singular series and automata</a>, manuscripta mathematica, Vol. 101 (2000), pp. 385-399.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler_product">Euler Product</a>.
%e 6.95743589392521746246609006782918530413...
%t $MaxExtraPrecision = 10000; Do[Print[5/2*Exp[-N[Sum[(-1)^j*6^j*(PrimeZetaP[2*j] - 1/4^j)/j, {j, 1, t}], 120]]], {t, 100, 1000, 100}] (* _Vaclav Kotesovec_, May 29 2020 *)
%o (PARI) prodeulerrat(1 + 6/p^2) \\ _Amiram Eldar_, Mar 17 2021
%Y Cf. A000040, A001248, A082020, A065474, A206256, A328017.
%K nonn,cons
%O 1,1
%A _Jude Thaddeus Poole Jr._, Andrew Hinton, Reid Huntley, May 26 2020
%E More terms from _Vaclav Kotesovec_, May 29 2020
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